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arXiv · 0906.1827

Estimates of holomorphic functions in zero-free domains

Alexander Borichev·Vesselin Petkov
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Abstract

We study functions f(z) holomorphic in the upper half plane and having no zeros when the imaginary part of z is between 0 and 1, and we obtain a lower bound for the modulus of f(z) in this strip. In our analysis we deal with scalar functions f(z) as well as with operator valued holomorphic functions I+A(z) assuming that A(z) is a trace class operator in the upper half plane and I+A(z) is invertible in the same strip and is unitary on the real line.

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Alexander Borichev, Vesselin Petkov. 2009-06-09. Estimates of holomorphic functions in zero-free domains. https://arxiv.org/abs/0906.1827

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